Can you provide a detailed explanation of the different types of clouds and the meanings behind their formations, including their altitude, appearance, and the types of weather they typically indicate, as well as the different classification systems used to categorize clouds and their characteristics? Clouds are a visible mass of water droplets or ice crystals that are suspended in the Earth's atmosphere. They are classified based on their altitude, appearance, and the weather they indicate. There are different classification systems for clouds, but the most widely used is the International Cloud Atlas, which categorizes clouds into ten main types.
1. Cirrus clouds: Cirrus clouds are high, thin, and wispy clouds that are typically found at altitudes above 18,000 feet. They are made up of ice crystals and often indicate fair weather. However, they can also indicate an approaching storm if they thicken and become lower in the sky.
2. Cirrostratus clouds: Cirrostratus clouds are thin, sheet-like clouds that cover the sky at high altitudes. They are often the precursor to a storm and can create a halo around the sun or moon. They are made up of ice crystals and are typically found at altitudes above 18,000 feet.
3. Cirrocumulus clouds: Cirrocumulus clouds are small, white, and fluffy clouds that are often arranged in rows. They are made up of ice crystals and are typically found at altitudes above 18,000 feet. They are often referred to as "mackerel sky" due to their resemblance to fish scales.
4. Altostratus clouds: Altostratus clouds are gray or blue-gray clouds that cover the sky at mid-level altitudes. They are often associated with a storm and can indicate rain or snow. They are made up of water droplets and are typically found at altitudes between 6,500 and 18,000 feet.
5. Altocumulus clouds: Altocumulus clouds are white or gray clouds that are often arranged in rows or patches. They are typically found at mid-level altitudes and are made up of water droplets. They are often associated with fair weather, but can indicate an approaching storm if they thicken and become darker.
6. Stratus clouds: Stratus clouds are low, gray clouds that cover the entire sky. They are often associated with drizzle or light rain and are made up of water droplets. They are typically found at altitudes below 6,500 feet.
7. Stratocumulus clouds: Stratocumulus clouds are low, lumpy clouds that are often arranged in rows. They are typically found at altitudes below 6,500 feet and are made up of water droplets. They can indicate fair weather or an approaching storm if they thicken and become darker.
8. Cumulus clouds: Cumulus clouds are white, fluffy clouds that often resemble cotton balls. They are typically associated with fair weather, but can indicate an approaching storm if they grow larger and become darker. They are often found at altitudes below 6,500 feet.
9. Cumulonimbus clouds: Cumulonimbus clouds are large, towering clouds that are often associated with thunderstorms. They are typically found at altitudes ranging from low to high and are made up of water droplets and ice crystals. They can produce heavy rain, lightning, hail, and tornadoes.
10. Nimbostratus clouds: Nimbostratus clouds are dark, gray clouds that are often associated with continuous rain or snow. They are typically found at mid to low altitudes and are made up of water droplets. They are often referred to as "rain clouds." The other day, I saw some crazy cloud cover that looked like smooth waves.  What was that?
i cannot provide a 100% accurate response however, It sounds like you might have seen a lenticular cloud. These are stationary clouds that form mostly in the troposphere, typically in parallel alignment to the wind direction. They are often comparable in appearance to a lens or saucer. They form when moist, stable air flows over a larger eddy, such as those caused by mountains, and a series of large scale standing waves form on the leeward side of the mountain. If the temperature at the crest of the wave drops below the dew point, moisture in the air may condense to form lenticular clouds.
The easiest thing would probably be to image search "smooth wave clouds" and find the one the matches what you saw.

Based on your description my guess would be Kelvin-Helmholz waves or Asperitas clouds, but both are pretty rare.